CN110704958B - Pre-internal force of multi-internal force component and calculation method thereof - Google Patents
Pre-internal force of multi-internal force component and calculation method thereof Download PDFInfo
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Abstract
The invention discloses a pre-internal force of a multi-internal force component and a calculation method thereof, wherein the pre-internal force comprises the steps of adjusting the connection state of at least one node of the multi-internal force component to be a first connection state, applying a pre-load to a structure where the multi-internal force component is positioned, and calculating the first internal force when the at least one node of the multi-internal force component is in the first connection state according to the applied pre-load; adjusting the connection state of at least one node of the multi-internal-force component from the first connection state to the second connection state, unloading the preload and applying load to the structure of the multi-internal-force component, and respectively calculating the second internal force and the third internal force when the at least one node of the multi-internal-force component is in the second connection state according to the unloaded preload and the applied load; and superposing the first internal force, the second internal force and the third internal force to obtain the target internal force. The theoretical calculation value of the internal force of the component calculated by the method is better than that of the traditional component which is homogenized, and the actual stressed deformation performance and economy of the component are better.
Description
Technical Field
The invention relates to the technical field of structural engineering, in particular to a pre-internal force of a multi-internal force component and a calculation method thereof.
Background
In practical applications, in order to determine the stress performance of an engineering structure, the internal forces (including shear force, axial force, torque, bending moment, etc.) of the engineering structure when bearing a load are generally calculated by analyzing and calculating before the construction (manufacturing) of the structure, so as to obtain theoretical calculation values. At present, all components are connected at one time to form a single state, all loads are applied, and theoretical calculation values of internal forces of the components are analyzed and calculated under the condition.
However, since the internal force distribution of the structure depends on the rigidity distribution, the connection state formed by the method is single, the rigidity is uneven, the internal force distribution of the structural member is uneven (mainly concentrated at a certain node or part with larger connection rigidity of a member with larger rigidity), if the internal force of the member is analyzed based on the theoretical calculation value, the stress performance of the erroneous judgment member in the structure is poor, the safety is insufficient, the structure of the member needs to be redesigned, for example, the internal force distribution is concentrated in the design of the member, the section needs to be increased, more materials need to be used, and the economy of the member is poor.
Disclosure of Invention
The embodiment of the invention discloses a pre-internal force of a multi-internal force component and a calculation method thereof.
The embodiment of the invention discloses a pre-internal force of a multi-internal force component and a calculation method thereof, comprising the following steps:
adjusting the connection state of at least one node of the multi-internal force member to be a first connection state, applying a preload to a structure in which the multi-internal force member is located, and calculating a first internal force when the at least one node of the multi-internal force member is in the first connection state according to the applied preload;
adjusting the connection state of the at least one node of the multi-internal force member from the first connection state to the second connection state, unloading the preload and applying a load to the structure of the multi-internal force member, and respectively calculating a second internal force and a third internal force when the at least one node of the multi-internal force member is in the second connection state according to the preload and the load applied;
and superposing the first internal force, the second internal force and the third internal force to obtain a target internal force.
Compared with the prior art, the embodiment of the invention has the following beneficial effects:
in this embodiment, the first internal force of the member is calculated by adjusting the connection state of at least one node of the member to be the first connection state and applying the preload, then adjusting the connection state of at least one node of the member to be the second connection state, removing the preload (i.e., applying the reverse preload) and applying the load, and calculating the second internal force and the third internal force of the member. And obtaining the target internal force by superposing the first internal force of the first connection state, the second internal force of the second connection state and the third internal force. According to the method, node connection rigidity of the structural member is generated in stages, preload is applied in stages corresponding to different connection rigidity, preload is removed, load is applied, accordingly, internal force distribution of the structural member can be effectively reduced, calculated internal force is homogenized compared with traditional internal force, and peak value is reduced. The internal force of the component is analyzed based on the internal force obtained by calculation, so that the feasibility of the stress of the component in the structure can be accurately judged, the distribution concentration of the internal force of the component is reduced, a proper section is selected, and the component economy is better.
Drawings
In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings that are needed in the embodiments will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and other drawings may be obtained according to these drawings without inventive effort for a person skilled in the art.
FIG. 1 is an internal force diagram of a conventional frame structure under load;
FIG. 2 is a flow chart of a pre-internal force and method of calculating the same for a multi-internal force member of the present disclosure;
FIG. 3 is a flow chart of step 101 of the present disclosure;
FIG. 4 is a flow chart of step 102 of the present disclosure;
FIG. 5 is a first internal force diagram of a frame structure under preload in accordance with one embodiment of the present invention;
FIG. 6 is a second internal force diagram of a frame structure under reverse preload in accordance with one embodiment of the present invention;
FIG. 7 is a pre-interior force diagram in case one after the superposition of FIGS. 5 and 6;
FIG. 8 is an intra-target force diagram in case one after the superposition of FIGS. 1 and 7;
FIG. 9 is a first internal force diagram of a frame structure under preload in case two of the present invention;
FIG. 10 is a second internal force diagram of a frame structure under reverse preload in case two of the present invention;
FIG. 11 is a pre-interior force diagram in case two after the superposition of FIGS. 9 and 10;
FIG. 12 is an intra-objective force diagram in case two after the superposition of FIGS. 1 and 11;
FIG. 13 is a first internal force diagram of a frame structure under preload in case three of the present invention;
FIG. 14 is a second internal force diagram of a frame structure under reverse preload in case three of the present invention;
FIG. 15 is a pre-interior force diagram in case three after the superposition of FIGS. 13 and 14;
fig. 16 is an intra-target force diagram in case three after the superposition of fig. 1 and 15.
Detailed Description
The following description of the embodiments of the present invention will be made clearly and completely with reference to the accompanying drawings, in which it is apparent that the embodiments described are only some embodiments of the present invention, but not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
In the present invention, the terms "upper", "lower", "left", "right", "front", "rear", "top", "bottom", "inner", "outer", "middle", "vertical", "horizontal", "lateral", "longitudinal" and the like indicate an azimuth or a positional relationship based on that shown in the drawings. These terms are only used to better describe the present invention and its embodiments and are not intended to limit the scope of the indicated devices, elements or components to the particular orientations or to configure and operate in the particular orientations.
Also, some of the terms described above may be used to indicate other meanings in addition to orientation or positional relationships, for example, the term "upper" may also be used to indicate some sort of attachment or connection in some cases. The specific meaning of these terms in the present invention will be understood by those of ordinary skill in the art according to the specific circumstances.
Furthermore, the terms "mounted," "configured," "provided," "connected," and "connected" are to be construed broadly. For example, it may be a fixed connection, a removable connection, or a unitary construction; may be a mechanical connection, or an electrical connection; may be directly connected, or indirectly connected through intervening media, or may be in internal communication between two devices, elements, or components. The specific meaning of the above terms in the present invention can be understood by those of ordinary skill in the art according to the specific circumstances.
Furthermore, the terms "first," "second," and the like, are used primarily to distinguish between different devices, elements, or components (the particular species and configurations may be the same or different), and are not used to indicate or imply the relative importance and number of devices, elements, or components indicated. Unless otherwise indicated, the meaning of "a plurality" is two or more.
The invention discloses a pre-internal force of a multi-internal force component and a calculation method thereof.
Referring to fig. 2 to fig. 4, a method for calculating a pre-internal force of a multi-internal force member according to an embodiment of the present invention includes:
101. adjusting the connection state of at least one node of the multi-internal force member to be a first connection state, applying a preload to the structure in which the multi-internal force member is located, and calculating a first internal force when the at least one node of the multi-internal force member is in the first connection state according to the applied preload.
In this embodiment, the multi-internal force member is a member in which at least two kinds of internal forces are generated under the load, that is, the generated internal forces include any two or more of internal forces such as shearing force, axial force, bending moment, torque, and the like. In the embodiment, the multi-internal-component is a beam column component of a frame structure, and in the frame structure, under the action of vertical load, the frame beam receives two internal forces of shearing force and bending moment, and belongs to a multi-internal-force component. And the frame column receives shearing force, axial force and bending moment, and belongs to a multi-internal force component.
Further, the first connection state is unconnected, hinged or semi-rigid. And in the first connection state, the engineering structure to which the multi-internal-force component belongs is a transient structure, a statically determined structure and a statically determined structure.
Specifically, as shown in fig. 3, the step 101 specifically includes the following steps:
1011. and analyzing the constraint total number when the node of the structure where the multi-internal force component is positioned is in the once generated connection state.
In this embodiment, the second connection state is hinged, semi-rigid or rigid, and the connection stiffness of the second connection state is greater than the connection stiffness of the first connection state. In the second connection state, the engineering structure of the multi-internal-force component is a statically indeterminate structure, and redundant constraint exists.
Further, the constraints include line constraints and/or angle constraints. In particular, the wire constraint is used to limit the linear displacement between the connected component and the component or the support, including axial displacement and lateral displacement. The angular constraint is used to limit the angular displacement between the connected component and the component or the support, including bending moment displacement and torque displacement. The linear and angular displacements can be classified into axial, lateral and bending and twisting constraints and correspond to the four internal forces of axial, shear, bending and torsion.
1012. Releasing constraints at least one node of the multi-internal force member, and the number of released constraints is less than the total number of constraints.
In this embodiment, the number of constraints when at least one node of the multi-internal-force member is in the second connection state is not less than the number of constraints of the connection state generated at one time by the structure in which the multi-internal-force member is located at the node thereof.
In this step 1012, the connection stiffness of the engineering structure of the multi-internal force member is reduced due to the release of some or all of the constraints of at least one node of the multi-internal force member. That is, the first connection state is formed by the second connection state by releasing part or all of the constraint (decreasing the connection rigidity). For example, when the second connection state is hinged, the second connection state is adjusted to the first connection state by releasing a part or all of the restraint of at least one node of the multi-internal force member, and the first connection state is unconnected. Likewise, when the second connection state is semi-rigid, the first connection state may be unconnected or hinged; when the second connection state is rigid connection, the first connection state can be unconnected, hinged or semi-rigid connection.
From the basic theory of structure, it is known that the force distribution in the structure is related to the structural rigidity distribution. The rigidity of the node and the component is high, and the internal force distribution is high. The node and the component with small rigidity have small internal force distribution. In order to make the internal force distribution of the multi-internal force member more uniform, this step 1012 is performed according to the inherent characteristics of the internal forces of the above structure. The stiffness of the node of the stiffer component is reduced, so that the larger internal force of the node is partially transferred to the node with smaller stiffness (smaller internal force), thereby realizing the transfer and redistribution of the internal force, reducing the peak value of the internal force and homogenizing the internal force.
1013. And calculating the load born by the nodes of the multi-internal-force component in the second connection state, and taking the preload value according to the load.
In this embodiment, the second connection state is the same as the connection state generated by the node of the multi-internal-force member at one time, and the load born by the second connection state is a load that may be applied in practical use, including a permanent load, a variable load, and an accidental load. Wherein, the permanent load comprises structural dead weight, soil pressure, prestress and the like, the variable load comprises floor live load, roof live load, accumulated ash load, crane load, wind load, snow load, temperature action and the like, and the accidental load comprises explosive force, impact force and the like. Based on the uncertainty of accidental loads, in the homogenization calculation, the accidental loads are removed for analysis calculation, namely the loads born by the multi-internal-force component mainly comprise permanent loads and variable loads. In this step 1013, the load is calculated by a theoretical calculation formula provided by the building structure load specification.
Further, the preload is in accordance with the direction of the load and distributes any load and/or effect, which may be the same or different.
As an alternative embodiment, the preload is the same as the distribution of the load, the preload being a pre-stack load or a pre-mount load.
As another alternative, the preload is different from the load distribution, and the preload includes any one or a combination of any plurality of distributed load, concentrated load, tension, compression, counter-tension, counter-compression.
1014. The preload is applied to the structure in which the multiple internal force member is located.
It is understood that the engineering structure of the multi-force member is generated in stages through the step 1012, the step 1013, and the step 1014, the first connection state is a first stage, and the preload is applied in the first stage.
1015. A first internal force of at least one node of the multi-internal force member in the first connection state is calculated based on the applied preload.
In step 1015, the first internal force may be analyzed and calculated according to the mechanical theory according to the preload and the first connection state.
102. And adjusting the connection state of at least one node of the multi-internal-force component from the first connection state to the second connection state, unloading the preload and applying load to the structure of the multi-internal-force component, and respectively calculating the second internal force and the third internal force when the at least one node of the multi-internal-force component is in the second connection state according to the unloaded preload and the applied load.
In this embodiment, as shown in fig. 4, the step 102 specifically includes the following steps:
1021. the released constraint at least one node of the multi-internal force member is re-added to adjust from the first connection state to the second connection state.
In this step 1021, the added constraint is not less than the released constraint, and the engineering structure to which the multi-internal force member belongs is adjusted to the second connection state by this step 1021.
1022. The reverse preload is determined based on the preload applied.
In this step 1022, the reverse preload is equal in magnitude and opposite in direction to the preload.
1023. The reverse preload and the load are applied to the structure in which the multi-internal force member is located.
It should be appreciated that the step 1023 is performed after the step 1021, i.e., the connection state of at least one node of the multi-force member has been adjusted from the first connection state to the second connection state when the step 1023 is performed. Based on mechanical theory, in the second connection state, the order of applying the reverse preload and the load may follow, since the order of applying the preload and the load does not affect the subsequent step 1024, i.e., the calculation of the second internal force and the third internal force. That is, the reverse preload may be applied first, followed by the load, or the load may be applied first, followed by the reverse preload, or both the reverse preload and the load may be applied simultaneously.
It can be appreciated that, through the steps 1021, 1022 and 1023, the engineering structure to which the multi-force member belongs is generated in stages, the second connection state is a second stage, and the reverse preload and the load are applied in the second stage.
Compared with the existing method for generating the engineering structure at one time and applying all loads, the method is characterized in that the engineering structure is generated in a first stage and a second stage, and the preload and the reverse preload are respectively applied in the first stage and the second stage. The internal force of the component can be homogenized, the amplitude of the internal force is reduced, the theoretical calculated value of the internal force of the component obtained by calculation is homogenized, the peak value is reduced, and the actual stressed deformation performance and the economy of the component are better.
1024. And respectively calculating a second internal force and a third internal force when the node of the multi-internal force component is in the second connection state according to the applied reverse preload and the load.
In step 1024, the second internal force and the third internal force may be analyzed and calculated according to the reverse preload, the load and the second connection state and the mechanical theory.
103. And superposing the first internal force, the second internal force and the third internal force to obtain a target internal force.
In this embodiment, the step 103 specifically includes:
1031. the first internal force and the second internal force are superimposed to obtain a pre-internal force.
In this embodiment, the first internal force is an internal force generated by the preload received by at least one node of the multi-internal force member in the first connection state, and the second internal force is an internal force generated by the reverse preload received by at least one node of the multi-internal force member in the second connection state. Since the reverse preload is equal in magnitude and opposite in direction to the preload. The reverse preload and the preload may cancel each other, i.e., the preload and the reverse preload are superimposed to zero, thereby zeroing the external load (load independent of the load to which the engineering structure is subjected in actual use). Since the first connection state and the second connection state are different, the direction of the internal force generated by the preload and the reverse preload is opposite, but the magnitude and distribution of the internal force are completely different, so that the internal forces generated by the preload and the reverse preload cannot be mutually offset, and the residual internal force after superposition is called as "pre-internal force".
1032. The pre-internal force and the third internal force are superimposed to obtain a target internal force.
In this step 1032, since the engineering structure is in the conventional once-generated connection state, the direction of the pre-internal force at the position where the internal force is large is opposite to the direction of the conventional internal force (third internal force), so that the conventional internal force at this position is reduced, and the direction of the pre-internal force at the position where the internal force is small is the same as the direction of the conventional internal force (third internal force), so that the conventional internal force at this position is increased, that is, the conventional internal force is redistributed and homogenized.
It will be appreciated that the present invention is primarily directed to a method of generating (e.g., dividing) the connection state of at least one node of a multi-internal force member in stages (e.g., into a first stage and a second stage) and applying a preload in the first stage, and unloading the preload in the second stage, and unloading the preload in the first stage and the preload in the second stage, wherein the external load is zeroed, but the internal forces generated by the respective external load are different due to the different structural states applied by the respective external load, so that the structure generates a "preload" that is beneficial to reducing the internal forces of the load.
The result of the pre-internal force measure is a reduction and homogenization of the conventional internal force. The degree of subtractive homogenization depends on the relative proportions of the different rigidities of the two stage states, as well as the method of the pre-internal force measures, the pre-tension distribution, the size and efficiency, etc. The control of the preload magnitude is mainly performed, that is, the preload is controlled to a certain ratio corresponding to the load to be applied, that is, the ratio of preload to load u=p/q, u being called "preload factor".
Wherein, the pre-internal force measure means: and the pre-load is applied when at least one node of the multi-internal force component is in the first connection state, and the pre-load is removed after the multi-internal force component is adjusted to the second connection state.
Taking a multi-internal-force beam column member in a frame structure as an example, the frame structure is symmetrical, the born load is vertical load and the distribution is asymmetric, and the internal force after the split-state pre-internal-force measure is adopted to subtract and homogenize is demonstrated and compared with the traditional internal force, and the demonstration is as follows:
by adopting a traditional calculation method, as shown in fig. 1, fig. 1 is a single-layer single-span frame, and the connection state of the single-layer single-span frame is generated at one time and all loads are applied at one time. In the calculation process, the frame beam is simply called a beam, and the frame column is simply called a column.
The column located on the left side of the frame structure (i.e., on the left side in the direction of the paper surface in fig. 1) is referred to as a column L, and the column on the right side is referred to as a column R, and in the case where at least one node of the multi-internal force member is in the second connection state, the number of constraints is equal to the number of constraints of the connection state generated at one time by the node of the multi-internal force member. At this time, the second connection state is a conventional connection state. .
The calculation is carried out according to engineering structure theory, and is carried out by a manual of static calculation of building structure (first edition 1975):
order the
I A ＝I B ＝I 1 ＝I 2 =i, h=l; the correlation coefficient is as follows:
μ 1 ＝2+K＝3
μ 2 ＝1+6K＝7
from the above coefficients, the following internal forces can be calculated:
1. the bending moment of the column top and the beam end is as follows:
2. the bending moment of the column root is as follows:
3. column shear force is:
4. the column axial force is:
as shown in fig. 1, in combination with the calculation results, it can be known that the horizontal shear force H of the column L and the column R in fig. 1 is equal, the column top bending moment of the column L and the column R are both much greater than the column root bending moment, the axial force and the bending moment of the column L are also much greater than the column R, and the beam D end bending moment and the shear force are both much greater than the beam E end. That is, the frame structure is generated and applied with all loads at one time by adopting a traditional calculation mode, and the calculated internal force distribution of the frame beam and the frame column is uneven.
Case one
In the first stage, as shown in fig. 5, step 101 is performed to adjust the connection state of the column top of the column L to be the first connection state and to be unconnected, and the load q borne by the node of the multi-internal-force member in the second connection state is known to be a half-span uniform load, and a preload p is applied to at least one node of the multi-internal-force member in the first connection state, wherein the applied preload p is consistent with the direction and distribution of the load q, so as to generate a preload internal force. The first internal force is calculated as follows:
1. the axial force of the column is equal to the vertical counter force of its support:
N Lp ＝V Ap ＝0
2. the shear force of the column is equal to the horizontal counter force of its support:
H Bp (H Ap )＝0
3. bending moment of the column:
M Ap ＝M Dp ＝0
4. bending moment in beam span:
in the second stage, as shown in fig. 6, the connection state of the column top of the column L is again adjusted to be the second connection state and is just connected, and a reverse preload p '(a unload preload p) is applied in the second connection state, wherein the reverse preload p' is equal to the preload p in magnitude and opposite in direction, and the generated internal force distribution is different. The second internal force is calculated as follows:
1. the axial force of the column is equal to the vertical counter force of its support:
2. the shear force of the column is equal to the horizontal counter force of its support:
3. bending moment of the column:
4. bending moment in beam span:
as shown in fig. 7, fig. 7 is a "preloaded pre-internal force map" obtained by superimposing the internal force map of the first internal force (fig. 5) and the internal force map of the second internal force (fig. 6), that is, performing step 1031, superimposing the first internal force and the second internal force to obtain the pre-internal force as follows:
1. the pre-shear force of columns L and R is:
it can be seen that the column L and the column R both generate a pre-shearing force in a direction opposite to the conventional shearing force by the pre-internal force measure, and the conventional shearing force of the column L and the column R can be reduced.
2. The pre-axial forces of columns L and R are:
it can be seen that, by the pre-internal force measure, the column L with a larger conventional axial force generates a pre-axial force opposite to the conventional axial force, so that the conventional axial force of the column L can be reduced, and the column R with a smaller conventional axial force generates a pre-axial force identical to the conventional axial force in direction, so that the conventional axial force of the column R can be increased.
3. The column top pre-bending moment (control bending moment) of the column L and the column R is:
it can be seen that by means of the pre-internal force measure, the column L with the larger conventional control bending moment generates a column top pre-bending moment opposite to the conventional control bending moment in direction, the conventional control bending moment of the column L can be reduced, the column R with the smaller conventional control bending moment generates a column top pre-bending moment identical to the conventional control bending moment in direction, and the conventional control bending moment of the column R can be increased.
4. The pre-bending moment (peak bending moment) in the beam span is:
it can be seen that the conventional bending moment of Liang Kuazhong can be reduced by generating a pre-bending moment in the beam span in the opposite direction to the conventional bending moment by the pre-internal force measure.
As can be seen from a combination of fig. 7 and the above calculation of the preload, from the first stage to the second stage, the reverse preload is applied such that the preload is completely zero. However, since the first connection state of the first stage is different from the second connection state of the second stage, the frame structure readjusts the receipt span frame by the cantilever beam frame (rigid frame), and the magnitude and distribution of the internal force generated by the preload and the reverse preload are different, so that the internal force cannot be offset, that is, the internal force is generated, and the conventional internal force can be reduced by the internal force, so that the internal force homogenization is realized.
Since the second connection state is the same as the connection state generated at one time by the node of the multi-internal force member, the third internal force calculated according to the load is a conventional internal force, and fig. 1 can be referred to.
As shown in fig. 8, fig. 8 is a two-state intra-structure force diagram of the preloaded pre-internal force obtained by superimposing the pre-internal force diagram of fig. 7 (preloaded pre-internal force diagram) and the conventional internal force diagram of fig. 1, that is, performing step 1032, superimposing the pre-internal force and the third internal force to obtain the target internal force as follows:
1. the column shear force is:
it can be seen that the shear force of the column is reduced compared with the shear force calculated by the traditional method when the method is implemented.
2. The axial force of the column is:
it can be seen that the axial force of the column L decreases and the axial force of the column R increases when the method of the present invention is carried out. Compared with the traditional calculation method, the axial force of the column L with larger axial force is reduced, the axial force of the column R with smaller axial force is increased, namely, the axial force of the column is transferred and redistributed, and the distribution of the axial force is more uniform.
3. Column top bending moment (control bending moment) of column:
it can be seen that the roof bending moment of the column L is reduced and the roof bending moment of the column R is increased by the method of the present invention. Compared with the traditional calculation method, the column top bending moment of the column L with larger column top bending moment is reduced, the column top bending moment of the column R with smaller column top bending moment is increased, namely, the column top bending moment of the column is transferred and redistributed, and the distribution of the column top bending moment is more uniform.
4. Beam span center bending moment (peak bending moment):
it can be seen that the mid-span bending moment of the beam is reduced compared with the bending moment calculated by the traditional method by implementing the method.
By the calculation method of the internal force of the multi-internal-force beam column component in the frame structure, the frame structure is generated in stages, the preload is applied in stages, the reverse preload and the load are applied in stages, the target internal force obtained by overlapping the internal forces in two stages is compared with the internal force calculated value obtained by the traditional method, and the following conclusion is reached: compared with the traditional frame structure, the axial force and the column top bending moment of the column with larger internal force are reduced, the axial force and the column top bending moment of the column with smaller internal force are increased, the bending moment of the beam is homogenized, and the midspan bending moment of the beam is reduced sharply. The theoretical calculation value of the internal force of the component calculated by the method is more ideal in distribution, and the actual stressed deformation performance and economy of the component are better.
Case two
Unlike case one, the preload applied in case two is different from the load distribution and is uniformly pretensioned, and the corresponding unloading is tension releasing (reverse pretensioning).
In the first stage, as shown in fig. 9, half-span uniform pretension p symmetrical to the load q is applied to generate pretension internal force distribution. The first internal force is calculated as follows:
1. the axial force of the column is equal to the vertical counter force of its support:
N Lp ＝V Ap ＝0
2. the shear force of the column is equal to the horizontal counter force of its support:
H Ap (H Bp )＝0
3. bending moment of the column:
M Ap ＝M Dp ＝0
4. bending moment in beam span:
M Cp ＝0
in the second stage, as shown in fig. 10, the connection state of the column top of the column L is again adjusted to be the second connection state and is just connected, and a reverse pretension p '(tension release) is applied in the second connection state, wherein the reverse pretension p' is equal to the pretension in magnitude and opposite in direction, and the generated internal force distribution is different. The second internal force is calculated as follows:
1. the axial force of the column is equal to the vertical counter force of its support:
2. the shear force of the column is equal to the horizontal counter force of its support:
3. bending moment of the column:
4. bending moment in beam span:
as shown in fig. 11, fig. 11 is a "uniformly pretensioned pre-force map" obtained by superimposing the internal force map 9 of the first internal force and the internal force map 10 of the second internal force, that is, performing step 1031, and superimposing the first internal force and the second internal force to obtain the pre-internal force as follows:
1. the pre-shear force of columns L and R is:
it can be seen that the column L and the column R both generate a pre-shearing force in a direction opposite to the conventional shearing force by the pre-internal force measure, and the conventional shearing force of the column L and the column R can be reduced.
2. The pre-axial forces of columns L and R are:
it can be seen that, by the pre-internal force measure, the column L having a larger conventional axial force generates a pre-axial force in the opposite direction to the conventional axial force, so that the conventional axial force of the column L can be reduced, and the column R having a smaller conventional axial force generates a pre-axial force in the opposite direction to the conventional axial force, so that the conventional axial force of the column R can be increased.
3. The column top pre-bending moment (control bending moment) of the column L and the column R is:
it can be seen that by means of the pre-internal force measure, the column L with the larger conventional control bending moment generates a column top pre-bending moment opposite to the conventional control bending moment in direction, the conventional control bending moment of the column L can be reduced, the column R with the smaller conventional control bending moment generates a column top pre-bending moment identical to the conventional control bending moment in direction, and the conventional control bending moment of the column R can be increased.
4. The pre-bending moment (peak bending moment) in the beam span is:
it can be seen that the conventional bending moment of Liang Kuazhong can be reduced by generating a pre-bending moment in the beam span in the opposite direction to the conventional bending moment by the pre-internal force measure.
As can be seen from a combination of fig. 11 and the above calculation of the pre-internal force, from the first stage to the second stage, the reverse pre-tension is applied such that the pre-tension is completely zeroed. However, since the first connection state of the first stage is different from the second connection state of the second stage, the frame structure is readjusted by the cantilever beam frame (rigid frame) to form a receipt span frame, and the internal forces generated by pretension and reverse pretension are different in magnitude and distribution and cannot be offset, that is, a pre-internal force is generated, and the pre-internal force can reduce the traditional internal force, so that internal force homogenization is realized.
As in case one, the target internal force is obtained by superimposing the pre-internal force map 11 (pre-tensioning pre-internal force map) and the uniformly pre-tensioned pre-internal force bi-state structural internal force map 12 obtained from the conventional internal force map 1, i.e. by implementing step 1032, by superimposing the pre-internal force and the third internal force as follows:
1. the column shear force is:
it can be seen that the shear force of the column is reduced compared with the shear force calculated by the traditional method when the method is implemented.
2. The axial force of the column is:
it can be seen that the axial force of the column L decreases and the axial force of the column R increases when the method of the present invention is carried out. Compared with the traditional calculation method, the axial force of the column L with larger axial force is reduced, the axial force of the column R with smaller axial force is increased, namely, the axial force of the column is transferred and redistributed, and the distribution of the axial force is more uniform.
3. Column top bending moment (control bending moment) of column:
it can be seen that the roof bending moment of the column L is reduced and the roof bending moment of the column R is increased by the method of the present invention. Compared with the traditional calculation method, the column top bending moment of the column L with larger column top bending moment is reduced, the column top bending moment of the column R with smaller column top bending moment is increased, namely, the column top bending moment of the column is transferred and redistributed, and the distribution of the column top bending moment is more uniform.
4. Beam span center bending moment (peak bending moment):
it can be seen that the mid-span bending moment of the beam is reduced compared with the bending moment calculated by the traditional method by implementing the method.
Case two can draw the same conclusion as case one: by implementing the calculation method of the invention, in the traditional frame structure, the axial force and the column top bending moment of the column with larger internal force are reduced, the axial force and the column top bending moment of the column with smaller internal force are increased, the bending moment of the beam is homogenized, and the midspan bending moment of the beam is reduced sharply. The theoretical calculation value of the internal force of the component calculated by the method is more ideal in distribution, and the actual stressed deformation performance and economy of the component are better.
Case three
Unlike case two, case three applies pretension as concentrated pretension.
In a first stage, shown in fig. 13, a concentrated pretension P is applied across the center, resulting in a pretension internal force distribution. The first internal force is calculated as follows:
1. the axial force of the column is equal to the vertical counter force of its support:
N LP ＝V AP ＝0
N RP ＝V BP ＝P
2. the shear force of the column is equal to the horizontal counter force of its support:
H AP (H BP )＝0
3. bending moment of the column:
M AP ＝M DP ＝0
4. bending moment in beam span:
M CP ＝0
in the second stage, as shown in fig. 14, the connection state of the column top of the column L is adjusted again to be the second connection state and is just connected, and a reverse pretension P 'is applied in the second connection state, wherein the reverse pretension P' is equal to the pretension in magnitude and opposite in direction, and an internal force distribution of the tension opposite to the conventional sign is generated. The second internal force is calculated as follows:
the calculation is carried out according to the building structure theory, and the method is carried out in a building structure static calculation manual (first edition in 1975):
1. the axial force of the column is equal to the vertical counter force of its support:
2. the shear force of the column is equal to the horizontal counter force of its support:
3. bending moment of the column:
4. bending moment in beam span:
as shown in fig. 15, the "concentrated pretensioned pre-force map" obtained by superimposing the first internal force map 13 and the second internal force map 14 of fig. 15, that is, performing step 1031, superimposes the first internal force and the second internal force to obtain the pre-internal force as follows:
1. the pre-shear force of columns L and R is:
it can be seen that the column L and the column R both generate a pre-shearing force in a direction opposite to the conventional shearing force by the pre-internal force measure, and the conventional shearing force of the column L and the column R can be reduced.
2. The pre-axial forces of columns L and R are:
it can be seen that, by the pre-internal force measure, the column L with a larger conventional axial force generates a pre-axial force opposite to the conventional axial force, so that the conventional axial force of the column L can be reduced, and the column R with a smaller conventional axial force generates a pre-axial force identical to the conventional axial force in direction, so that the conventional axial force of the column R can be increased.
3. The column top pre-bending moment (control bending moment) of the column L and the column R is:
it can be seen that by means of the pre-internal force measure, the column L with the larger conventional control bending moment generates a column top pre-bending moment opposite to the conventional control bending moment in direction, the conventional control bending moment of the column L can be reduced, the column R with the smaller conventional control bending moment generates a column top pre-bending moment identical to the conventional control bending moment in direction, and the conventional control bending moment of the column R can be increased.
4. The pre-bending moment (peak bending moment) in the beam span is:
it can be seen that the conventional bending moment of Liang Kuazhong can be reduced by generating a pre-bending moment in the beam span in the opposite direction to the conventional bending moment by the pre-internal force measure.
As can be seen from the calculation of the pre-internal force in combination with fig. 15 and above, from the first stage to the second stage, a reverse pre-tension is applied such that the pre-tension is completely zero, without an external load. However, since the first connection state of the first stage is different from the second connection state of the second stage, the frame structure is readjusted by the cantilever beam frame (rigid frame) to form a receipt span frame, and the internal forces generated by pretension and reverse pretension are different in magnitude and distribution and cannot be offset, that is, a pre-internal force is generated, and the pre-internal force can reduce the traditional internal force, so that internal force homogenization is realized.
As in case two, the target internal force is obtained by superimposing the pre-internal force map 15 (pre-tension pre-internal force map) and the concentrated pre-internal force bi-state structure internal force map 16 obtained from the conventional internal force map 1, i.e., performing step 1032, by superimposing the pre-internal force and the third internal force as follows:
1. the column shear force is:
it can be seen that the shear force of the column is reduced compared with the shear force calculated by the traditional method when the method is implemented.
2. The axial force of the column is:
it can be seen that the axial force of the column L decreases and the axial force of the column R increases when the method of the present invention is carried out. Compared with the traditional calculation method, the axial force of the column L with larger axial force is reduced, the axial force of the column R with smaller axial force is increased, namely, the axial force of the column is transferred and redistributed, and the distribution of the axial force is more uniform.
3. Column top bending moment (control bending moment) of column:
it can be seen that the roof bending moment of the column L is reduced and the roof bending moment of the column R is increased by the method of the present invention. Compared with the traditional calculation method, the column top bending moment of the column L with larger column top bending moment is reduced, the column top bending moment of the column R with smaller column top bending moment is increased, namely, the column top bending moment of the column is transferred and redistributed, and the distribution of the column top bending moment is more uniform.
4. Beam span center bending moment (peak bending moment):
it can be seen that the mid-span bending moment of the beam is reduced compared with the bending moment calculated by the traditional method by implementing the method.
Case three can draw the same conclusion as case one and case two: by implementing the calculation method of the invention, in the traditional frame structure, the axial force and the column top bending moment of the column with larger internal force are reduced, the axial force and the column top bending moment of the column with smaller internal force are increased, the bending moment of the beam is homogenized, and the midspan bending moment of the beam is reduced sharply. The theoretical calculation value of the internal force of the component calculated by the method is more ideal, and the actual stressed deformation performance and economy of the component are better.
By combining the cases, the method of the invention generates the node connection rigidity of the component in stages, and applies preload in stages corresponding to different connection rigidity, removes preload and applies load, thereby effectively homogenizing the internal force distribution of the component, and the calculated internal force distribution is more ideal. The internal force of the component is analyzed based on the internal force obtained by calculation, and the feasibility of the stress performance of the component in the structure can be accurately judged, so that the section of the component is accurately designed, the internal force distribution of the component is weakened, the selected section is more proper, and the component economy is better.
The above describes in detail the pre-internal force of a multi-internal force member and the calculating method thereof disclosed in the embodiments of the present invention, and the principles and embodiments of the present invention are described herein by applying examples, where the descriptions of the above examples are only used to help understand the pre-internal force of a multi-internal force member, the calculating method thereof and the core idea thereof; meanwhile, as those skilled in the art will have variations in the specific embodiments and application scope in accordance with the ideas of the present invention, the present description should not be construed as limiting the present invention in view of the above.
Claims (9)
1. A method for calculating the pre-internal force of a multi-internal force component is characterized by comprising the following steps:
adjusting the connection state of at least one node of the multi-internal force member to be a first connection state, applying a preload to a structure in which the multi-internal force member is located, and calculating a first internal force when the at least one node of the multi-internal force member is in the first connection state according to the applied preload;
adjusting the connection state of the at least one node of the multi-internal-force component again to adjust the connection state from the first connection state to a second connection state;
determining a reverse preload based on the preload applied;
applying the reverse preload and load to a structure in which the multi-internal force member is located;
calculating a second internal force and a third internal force of the multi-internal force member when the at least one node is in the second connection state according to the applied reverse preload and the load, respectively;
superposing the first internal force, the second internal force and the third internal force to obtain a target internal force;
the reverse preload is equal to the preload in magnitude and opposite in direction.
2. The method of claim 1, wherein the first connection state is unconnected, hinged, or semi-rigid, the second connection state is hinged, semi-rigid, or rigid, and the connection stiffness of the second connection state is greater than the connection stiffness of the first connection state.
3. A method according to claim 1, wherein the preload is in accordance with the direction of the load and any load and/or effect is distributed the same or different.
4. A method according to claim 3, wherein the preload is the same as the load distribution, the preload being a pre-stack load or a pre-mount load; or,
the preload is different from the load distribution, and the preload includes any one or a combination of any plurality of distributed load, concentrated load, tension, compression, counter-tension, counter-compression.
5. The method according to any one of claims 1 to 4, wherein said adjusting the connection state of at least one node of the multi-internal force member to a first connection state applies a preload to the structure in which the multi-internal force member is located, and calculating a first internal force of the at least one node of the multi-internal force member in the first connection state based on the preload applied comprises:
analyzing the constraint total number of the structure of the multi-internal-force component when the node is in a once-generated connection state;
releasing constraints at the at least one node of the multi-internal force member, and the number of released constraints is less than the total number of constraints;
calculating the load born by the at least one node of the multi-internal-force component in the second connection state, and taking the preload value according to the load;
applying the preload to a structure in which the multiple internal force member is located;
calculating a first internal force of the at least one node of the multi-internal force member in the first connection state based on the preload applied.
6. The method of claim 5, wherein readjusting the connection state of the at least one node of the multi-internal force member from the first connection state to a second connection state comprises:
the constraint released at the at least one node of the multi-internal force member is re-added to adjust from the first connection state to a second connection state.
7. The method of claim 6, wherein the constraints comprise line constraints and/or angle constraints.
8. The method of claim 1, wherein the multi-internal force member is a member having at least two different types of internal forces.
9. The method of any one of claims 1 to 4, wherein the number of constraints of the at least one node of the multi-internal force member when in the second connected state is not less than the number of constraints of the connected state that the structure in which the multi-internal force member is located generates at one time at the node thereof.
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| CN103488909A (en) * | 2013-10-15 | 2014-01-01 | 同济大学建筑设计研究院(集团)有限公司 | Virtual-load-based structure internal force calculation method in construction process |
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| CN105760691A (en) * | 2016-03-04 | 2016-07-13 | 西北农林科技大学 | Method for calculating internal force and deformation of member or structure under action of multiple complex loads |
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